How to create a slice effect on a Cylinder mesh
Here is a way to do it, but it's not mesh. I used a bezier circle and a curve.
I lined them up as shown in the first picture and pressed Control A and selected Rotation and Scale, to apply rotation and scale.

Then I had to make a break in the circle and as you can see in the second picture, I didn't line up the last control point with the first control point - left it carelessly placed so you can see it's not a proper circle.

To make the break in the circle, I went to Edit Mode, selected two adjacent control points and pressed Delete, then chose Segment.  Now with just one of those control points selected, I pressed Control and clicked with the Left Mouse button near the other vertex at the other end of the "missing segment".  Now you need to place the control point carefully and straighten the handles so they're perfectly horizontal or vertical.

Select the circle, go to Bevel, click on the eyedropper and then on the curve.
Then you can play with the Start and End sliders to open this cylinder along it's long axis.

You can assign a Solidify modifier at the end.





EDIT:
I've thought of a way of doing it with mesh using a Plane or flattened Cube (with enough segments to bend on the axis you need, and a Bezier Circle. With a Curve Modifier on the Plane, and the Bezier Circle selected as Object, and the appropriate Deformation Axis chosen, you can scale the Plane to make it fill out the Circle, and scale it back again to make it open up.